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%I #9 Nov 04 2021 20:47:33
%S 5,7,11,13,17,25,29,35,41,49,55,59,65,71,77,85,89,91,95,101,115,119,
%T 121,125,131,143,145,155,161,167,169,173,175,185,187,203,205,209,215,
%U 221,227,235,245,253,265,275,287,289,293,295,305,319,323,325,329,343,355,361,365,377,383,385,391,413,415,425,445,451
%N Numbers k congruent to 1 or 5 mod 6, for which A064989(A064989(sigma(k^2))) > A064989(A064989(k^2)), where A064989 shifts the prime factorization one step towards lower primes, and sigma is the sum of divisors function.
%C Square roots of squares present in A348754.
%C See comments in A348935.
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%t f[2, e_] := 1; f[p_, e_] := NextPrime[p, -1]^e; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[450], MemberQ[{1, 5}, Mod[#, 6]] && s[s[DivisorSigma[1, #^2]]] > s[s[#^2]] &] (* _Amiram Eldar_, Nov 04 2021 *)
%o (PARI)
%o A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o isA348936(n) = ((n%2)&&(n%3)&&(A064989(A064989(sigma(n^2))) > A064989(A064989(n^2))));
%Y Cf. A000203, A003961, A007310, A064989, A348750, A348754, A348934, A348935.
%K nonn
%O 1,1
%A _Antti Karttunen_, Nov 04 2021
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